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User blog:Username5243/Strong Array Notation googolisms I
Okay, here we go. This list is ridiculously long list, so I'm splitting it up. Part I: Three-Entry Level Regiments: 10 Goosol Regiment Group 1 s(a,b) Order type 2 Members: 35 (1 - 35) First we'll cover the two-entry level. s(a,b) is defined as a^b. Therefore we can define: (1) Goosol = s(10,100) To change the second argument, We use Latin names, like: (2) Goosoluni = s(10,1) = 10 (3) Goosolbi = s(10,2) = 100 (4) Goosoltri = s(10,3) = 1000 (5) Goosolquad = s(10,4) (6) Goosolquin = s(10,5) ... (7) Goosoldec = s(10,10) (8) Goosolvigint = s(10,20) (9) Goosoltrigint = s(10,30) (10) Goosolquinquagint = s(10,50) (11) Goosolcent = s(10,100) (12) Goosolducent = s(10,200) (13) Goosolquingent = s(10,500) (14) Goosolmil = s(10,1000) (15) Goosolmyr = s(10,10000) How to go further? By adding the plex operator which makes n into s(10,n). If a base-modifier is being applied, place it after the plex. (16) Goosolplexuni = s(10,10) (17) Goosolplexibi = s(10,100) (18) Goosolplexitri = s(10,1000) (19) Goosolplexiquin = s(10,s(10,5)) (20) Goosolplexidec = s(10,s(10,10)) (21) Goosolplexivigint = s(10,s(10,20)) (22) Goosolplex = s(10,s(10,100)) (23) Goosolpleximil = s(10,s(10,1000)) (24) Goosolpleximyr = s(10,s(10,10000)) Now we can have duplex, triplex, quadriplex, etc. (25) Goosolduplexuni = s(10,s(10,10)) (26) Goosolduplex = s(10,s(10,s(10,100))) (27) Goosoldupleximil = s(10,s(10,s(10,1000))) (28) Goosoldupleximyr = s(10,s(10,10000)) (29) Goosoltriplex = s(10,googolplex) (30) Goosolquadriplex = s(10,googoltriplex) (31) Goosolquintiplex = s(10,googolquadriplex) (32) Goosolsextiplex = s(10,googolquintiplex) (33) Goosolseptiplex = s(10,googolsextiplex) (34) Goosoloctiplex = s(10,googolseptiplex) (35) Goosolnoniplex = s(10,googoloctiplex) ... These numbers are already huge by most standards, But compared to what's to come, they're extremely tiny... Gransol Regiment Group 2 s(a,b,2) Order type 3 Members: 41 (36 - 76) Now we reach s(a,b,2). To solve this, we first consider the case s(a,1,2). Since none of the rules apply we use the process. The process says to find the first non-1 entry from the third entry - which is the 2 - and replace the "1,2" by "b,1". So s(a,1,2) = s(a,1,1) (in this case the second entry stays the same) = a. Then s(a,2,2) = s(a,s(a,1,2),1) = s(a,a) = a^a, s(a,3,2) = s(a,a^a) = a^^3, etc. This is basically titration. With this in mind, I define: (36) Gransol = s(10,100,2) = 10^^100 ...Then we form: (37) Gransoluni = s(10,1,2) (38) Gransolbi = s(10,2,2) (39) Gransoltri = s(10,3,2) (40) Gransolquin = s(10,5,2) (41) Gransoldec = s(10,10,2) (42) Gransolvigint = s(10,20,2) (43) Gransolquinquagint = s(10,50,2) (44) Gransolducent = s(10,200,2) (45) Gransolmil = s(10,1000,2) (46) Gransolmyr = s(10,10000,2) We now need a suffix to indicate s(10,n,2). We can't use plex here, as we'd get: (47) Gransolplex = s(10,gransol) = s(10,101,2) (48) Gransolduplex = s(10,102,2) (49) Gransoltriplex = s(10,103,2) Therefore I use dex. Let's apply the dex suffix to some of our googolisms. Note that we can also form even more mixed googolisms than what's shown here. (50) Goosoldexuni = s(10,10,2) (51) Goosoldexidec = s(10,10^10,2) (52) Goosoldex = s(10,s(10,100),2) = s(10,goosol,2) = 10^^10^100 (53) Goosoldexiplex = s(10,goosoldex) (54) Goosoldexiduplex = s(10,goosoldexiplex) (55) Goosoldeximil = s(10,s(10,1000),2) (56) Goosoldeximyr = s(10,s(10,10000),2) (57) Goosolplexidexidec = s(10,s(10,s(10,10)),2) (58) Goosolplexidex = s(10,goosolplex,2) (59) Goosolplexidexiplex = s(10,goosolplexidex) (60) Goosolduplexidex = s(10,goosolduplex,2) (61) Goosoltriplexidex = s(10,goosoltriplex,2) (62) Gransoldexuni = s(10,10,2) (63) Gransoldexiquin = s(10,s(10,5,2),2) (64) Gransoldexidec = s(10,s(10,10,2),2) (65) Gransoldex = s(10,s(10,100,2),2) = s(10,gransol,2) = 10^^10^^100 (66) Gransoldexiplex = s(10,gransoldex) (67) Gransolplexidex = s(10,s(10,101,2),2) (68) Goosoldudex = s(10,goosoldex,2) (69) Goosolplexidudex = s(10,goosolplexidex,2) (70) Goosolduplexidudex = s(10,goosolduplexidex,2) (71) Gransoldudex = s(10,gransoldex,2) (72) Goosoltridex = s(10,goosoldudex,2) (73) Goosolplexitridex = s(10,goosolplexidudex,2) (74) Gransoltridex = s(10,gransoldudex,2) (75) Gransolquadridex = s(10,gransoltridex,2) (76) Gransolquintidex = s(10,gransolquadridex,2) ... Greasol Regiment Group 3 s(a,b,3) Order Type 4 Members: 40 (77 - 116) Now for the next level. Let's begin by calculating what s(a,b,3) means. s(a,1,3) = s(a,1,2) = a, s(a,2,3) = s(a,s(a,1,3)),2) = s(a,a,2) = a^^a, s(a,3,3) = s(a,a^^a,2) = a^^^3, etc. This is pentation. (77) Greasol = s(10,100,3) = 10^^^100 (78) Greasoluni = s(10,1,3) (79) Greasolquin = s(10,5,3) (80) Greasoldec = s(10,10,3) (81) Greasolmil = s(10,1000,3) (82) Greasolmyr = s(10,10000,3) (83) Greasolplex = s(10,s(10,100,3)) (84) Greasolduplex = s(10,greasolplex) (85) Greasoldex = s(10,101,3) (86) Greasoldexiplex = s(10,greaspldex) (87) Greasolplexidex = s(10,greasolplex,2) (88) Greasoldudex = s(10,102,3) (89) Goosolthrex = s(10,s(10,100),3) (90) Goosolthrexiplex = s(10,goosolthrex) (91) Goosolthrexidex = s(10,goosolthrex,2) (92) Goosolplexithrex = s(10,goosolplex,3) (93) Goosolduplexithrex = s(10,goosolduplex,3) (94) Gransolthrex = s(10,s(10,100,2),3) (95) Gransolthrexiplex = s(10,gransolthrex) (96) Goosoldexithrex = s(10,goosoldex,3) (97) Gransolthrexidex = s(10,gransolthrex,2) (98) Gransolplexithrex = s(10,gransolplex,3) (99) Goosolplexidexithrex = s(10,goosolplexidex,3) (100) Gransoldexithrex = s(10,gransoldex,3) (101) Goosoldudexithrex = s(10,goosoldudex,3) (102) Gransoldudexithrex = s(10,gransoldudex,3) (103) Greasolthrex = s(10,s(10,100,3),3) (104) Greasolthrexiplex = s(10,greasolthrex) (105) Greasolthrexidex = s(10,greasolthrex,2) (106) Greasolplexithrex = s(10,greasolplex,3) (107) Greasoldexithrex = s(10,greaspldex,3) (108) Goosolduthrex = s(10,goosolthrex,3) (109) Goosolplexiduthrex = s(10,goosolplexithrex,3) (110) Gransolduthrex = s(10,gransolthrex,3) (111) Gransoldexiduthrex = s(10,gransoldexithrex,3) (112) Greasolduthrex = s(10,greasolthrex)3) (113) Goosoltrithrex = s(10,goosolduthrex,2) (114) Gransoltrithrex = s(10,gransolduthrex,3) (115) Greasoltrithrex = s(10,greasolduthrex,3) (116) Greasolquadrithrex = s(10,greasoltrithrex,3) ... Gigansol Regiment Group 4 s(a,b,4) Order Type 5 Members: 23 (117 - 139) At this point the pattern should be familiar. Each increment to the third argument adds an arrow. So: (117) Gigansol = s(10,100,4) = 10^^^^100 (118) Gigansoluni = s(10,1,4) (119) Gigansoldec = s(10,10,4) (120) Gigansolmil = s(10,1000,4) (121) Gigansolmyr = s(10,10000,4) (122) Gigansolplex = s(10,gigansol) (123) Gigansoldex = s(10,gigansol,2) (124) Gigansolthrex = s(10,101,4) (125) Goosoltetrex = s(10,s(10,100),4) (126) Goosolplexitetrex = s(10,googolplex,4) (127) Gransoltetrex = s(10,s(10,100,2),4) (128) Goosoldexitetrex = s(10,goosoldex,4) (129) Gransoldexitetrex = s(10,gransoldex,4) (130) Greasoltetrex = s(10,s(10,100,3),4) (131) Goosolthrexitetrex = s(10,goosolthrex,4) (132) Gransolthrexitetrex = s(10,gransolthrex,4) (133) Greasolthrexitetrex = s(10,greasolthrex,4) (134) Gigansoltetrex = s(10,s(10,100,4),4) (135) Goosoldutetrex = s(10,goosoltetrex,4) (136) Gransoldutetrex = s(10,gransoltetrex,4) (137) Greasoldutetrex = s(10,greasoltetrex,4) (138) Gigansoldutetrex = s(10,gigansoltetrex,4) (139) Gigansoltritetrex = s(10,gigansoldutetrex,4) ... Gorgesol Regiment Group 5 s(a,b,5) Order Type 6 Members: 30 (140 - 169) At this point we have a routine established. Let's get going with the fifth regiment: (140) Gorgesol = s(10,100,5) = 10^^^^^100 (141) Gorgesoluni = s(10,1,5) (142) Gorgesoldec = s(10,10,5) (143) Gorgesolmil = s(10,1000,5) (144) Gorgesolmyr = s(10,10000,5) (145) Gorgesolplex = s(10,gorgesol) (146) Gorgesoldex = s(10,gorgesol,2) (147) Gorgesolthrex = s(10,gorgesol,3) (148) Gorgesoltetrex = s(10,gorgesol,4) (149) Goosolpentex = s(10,s(10,100),5) (150) Goosolplexipentex = s(10,googolplex,2) (151) Gransolpentex = s(10,s(10,100,2),5) (152) Goosoldexipentex = s(10,goosoldex,5) (153) Gransoldexipentex = s(10,gransoldex,5) (154) Greasolpentex = s(10,s(10,100,3),5) (155) Goosolthrexipentex = s(10,goosolthrex,5) (156) Gransolthrexipentex = s(10,gransolthrex,5) (157) Greasolthrexipentex = s(10,greasolthrex,5) (158) Gigansolpentex = s(10,s(10,100,4),5) (159) Goosoltetrexipentex = s(10,gigansoltetrex,5) (160) Gransoltetrexipentex = s(10,gransoltetrex,5) (161) Greasoltetrexipentex = s(10,greasoltetrex,5) (162) Gigansoltetrexipentex = s(10,gigansoltetrex,5) (163) Gorgesolpentex = s(10,s(10,100,5),5) (164) Goosoldupentex = s(10,goosolpentex,5) (165) Gransoldupentex = s(10,gransolpentex,5) (166) Greasoldupentex = s(10,greasolpentex,5) (167) Gigansoldupentex = s(10,gigansolpentex,5) (168) Gorgesoldupentex = s(10,gorg esolpentex,5) (169) Gorgesoltripentex = s(10,gorgesoldupentex,5) ... Gulsol Regiment Group 6 s(a,b,6) Order Type 7 Members: 28 (170 - 197) ...On we go to the sixth level: (170) Gulsol = s(10,100,6) = 10{6}100 (171) Gulsoluni = s(10,1,6) (172) Gulsoldec = s(10,10,6) (173) Gulsolmil = s(10,1000,6) (174) Gulsolmyr = s(10,10000,6) (175) Gulsolplex = s(10,gulsol) (176) Gulsoldex = s(10,gulsol,2) (177) Gulsolthrex = s(10,gull,3) (178) Gulsoltetrex = s(10,gulsol,4) (179) Gulsolpentex = s(10,gull,5) (180) Goosolhex = s(10,s(10,100),6) (181) Goosolplexihex = s(10,goosolplex,6) (182) Gransolhex = s(10,s(10,100,2),6) (183) Gransoldexihex = s(10,gransoldex,6) (184) Greasolhex = s(10,s(10,100,3),6) (185) Greasolthrexihex = s(10,greasolthrex,6) (186) Gigansolhex = s(10,s(10,100,4),6) (187) Gigansoltetrexihex = s(10,gigansoltetrex,6) (188) Gorgesolhex = s(10,gorgesol,6) (189) Gorgesolpentexihex = s(10,gorgesolpentex,6) (190) Gulsolhex = s(10,s(10,100,6),6) (191) Goosolduhex = s(10,goosolhex,6) (192) Gransolduhex = s(10,gransolhex,6) (193) Greasolduhex = s(10,greasolhex,6) (194) Gigansolduhex = s(10,giganslohex,6) (195) Gorgesolduhex = s(10,gorgesolhex,6) (196) Gulsolduhex = s(10,gulsolhex,6) (197) Gulsoltrihex = s(10,gulsolduhex,6) ... Gaspsol Regiment Group 7 s(a,b,7) Order Type 8 Members: 25 (198 - 222) Now for the seventh level: (198) Gaspsol = s(10,100,7) = 10{7}100 (199) Gaspsoluni = s(10,1,7) (200) Gaspsoldec = s(10,10,7) (201) Gaspsolmil = s(10,1000,7) (202) Gaspsolmyr = s(10,10000,7) (203) Gaspsolplex = s(10,gaspsol) (204) Gaspsoldex = s(10,gaspsol,2) (205) Gaspsolthrex = s(10,gaspsol,3) (206) Gaspsoltetrex = s(10,gaspsol,4) (207) Gaspsolpentex = s(10,gaspsol,5) (208) Gaspsolhex = s(10,gaspsol,6) (209) Goosolheptex = s(10,s(10,100),7) (210) Goosolplexiheptex = s(10,goosolplex,7) (211) Gransolheptex = s(10,s(10,100,2),7) (212) Gransoldexiheptex = s(10,gransoldex,7) (213) Greasolheptex = s(10,s(10,100,3),7) (214) Greasolthrexiheptex = s(10,greasolthrex,7) (215) Gigansolheptex = s(10,s(10,100,4),7) (216) Gigansoltetrexiheptex = s(10,gigansoltetrex,7) (217) Gorgesolheptex = s(10,s(10,100,5),7) (218) Gorgesolpentexiheptex = s(10,gorgesolpentex,7) (219) Gulsolheptex = s(10,s(10,100,6),7) (220) Gulsolhexiheptex = s(10,gulsolhex,7) (221) Gaspsolheptex = s(10,s(10,100,7),7) (222) Gaspsolduheptex = s(10,gaspsolheptex,7) ... Ginorsol Regiment Group 8 s(a,b,8) Order Type 9 Members: 28 (223 - 250) And then comes the eighth: (223) Ginorsol = s(10,100,8) = 10{8}100 (224) Ginorsoluni = s(10,1,8) (225) Ginorsoldec = s(10,10,8) (226) Ginorsolmil = s(10,1000,8) (227) Ginorsolmyr = s(10,10000,8) (228) Ginorsolplex = s(10,ginorsol) (229) Ginorsoldex = s(10,ginorsol,2) (230) Ginorsolthrex = s(10,ginorsol,3) (231) Ginorsoltetrex = s(10,ginorsol,4) (232) Ginorsolpentex = s(10,ginorsol,5) (233) Ginorsolhex = s(10,ginorsol,6) (234) Ginorsolheptex = s(10,ginorsol,7) (235) Goosoloctex = s(10,s(10,100),8) (236) Goosolplexoctex = s(10,goosolplex,8) (237) Gransoloctex = s(10,s(10,100,2),8) (238) Gransoldexoctex = s(10,gransoldex,8) (239) Greasoloctex = s(10,s(10,100,3),8) (240) Greasolthrexoctex = s(10,greasolthrex,8) (241) Gigansoloctex = s(10,s(10,100,4),8) (242) Gigansoltetrexoctex = s(10,gigansoltetrex,8) (243) Gorgesoloctex = s(10,s(10,100,5),8) (244) Gorgesolpentexoctex = s(10,gorgesolpentex,8) (245) Gulsoloctex = s(10,s(10,100,6),8) (246) Gulsolhexoctex = s(10,gulsolhex,8) (247) Gaspsoloctex = s(10,s(10,100,7),8) (248) Gaspsolheptexoctex = s(10,gaspsolheptex,8) (249) Ginorsoloctex = s(10,s(10,100,8),8) (250) Ginorsolduoctex = s(10,ginorsoloctex,8) ... Gargansol Regiment Group 9 s(a,b,9) Order Type 10 Members: 31 (251 - 281) And then the ninth: (251) Gargansol = s(10,100,9) = 10{9}100 (252) Gargansoluni = s(10,1,9) (253) Gargansoldec = s(10,10,9) (254) Gargansolmil = s(10,1000,9) (255) Gargansolmyr = s(10,10000,9) (256) Gargansolplex = s(10,gargansol) (257) Gargansoldex = s(10,gargansol,2) (258) Gargansolthrex = s(10,gargansol,3) (259) Gargansoltetrex = s(10,gargansol,4) (260) Gargansolpentex = s(10,gargansol,5) (261) Gargansolhex = s(10,gargansol,6) (262) Gargansolheptex = s(10,gargansol,7) (263) Gargansoloctex = s(10,gargansol,8) (264) Goosolennex = s(10,s(10,100),9) (265) Goosolplexennex = s(10,goosolplex,9) (266) Gransolennex = s(10,s(10,100,2),9) (267) Gransoldexennex = s(10,gransoldex,9) (268) Greasolennex = s(10,s(10,100,3),9) (269) Greasolthrexennex = s(10,greasolthrex,9) (270) Gigansolennex = s(10,s(10,100,4),9) (271) Gigansoltetrexennex = s(10,gigansoltetrex,9) (272) Gorgesolennex = s(10,s(10,100,5),9) (273) Gorgesolpentexennex = s(10,gorgesolpentex,9) (274) Gulsolennex = s(10,s(10,100,6),9) (275) Gulsolhexennex = s(10,gulsolhex,9) (276) Gaspsolennex = s(10,s(10,100,7),9) (277) Gaspsolheptexennex = s(10,gaspsolheptex,9) (278) Ginorsolennex = s(10,s(10,100,8),9) (279) Ginorsoloctexennex = s(10,ginorsoloctex,9) (280) Gargansolennex = s(10,s(10,100,9),9) (281) Gargansolduennex = s(10,gargansolennex,9) ... Googonsol Regiment Group 10 s(a,b,10) Order Type 11 Members: 34 (282 - 315) And finally the tenth: (282) Googonsol = s(10,100,10) = 10{10}100 (283) Googonsoluni = s(10,1,10) (284) Googonsoldec = s(10,10,10) (285) Googonsolmil = s(10,1000,10) (286) Googonsolmyr = s(10,10000,10) (287) Googonsolplex = s(10,googonsol) (288) Googonsoldex = s(10,googonsol,2) (289) Googonsolthrex = s(10,googonsol,3) (290) Googonsoltetrex = s(10,googonsol,4) (291) Googonsolpentex = s(10,googonsol,5) (292) Googonsolhex = s(10,googonsol,6) (293) Googonsolheptex = s(10,googonsol,7) (294) Googonsoloctex = s(10,googonsol,8) (295) Googonsolennex = s(10,googonsol,9) (296) Goosoldecex = s(10,s(10,100),10) (297) Goosolplexidecex = s(10,goosolplex,10) (298) Gransoldecex = s(10,s(10,100,2),10) (299) Gransoldexidecex = s(10,gransoldex,10) (300) Greasoldecex = s(10,s(10,100,3),10) (301) Greasolthrexidecex = s(10,greasolthrex,10) (302) Gigansoldecex = s(10,s(10,100,4),10) (303) Gigansoltetrexidecex = s(10,gigansoltetrex,10) (304) Gorgesoldecex = s(10,s(10,100,5),10) (305) Gorgesolpentexidecex = s(10,gorg esolpentex,10) (306) Gulsoldecex = s(10,s(10,100,6),10) (307) Gulsolhexidecex = s(10,gulsolhex,10) (308) Gaspsoldecex = s(10,s(10,100,7),10) (309) Gaspsolheptexidecex = s(10,gaspsolheptex,10) (310) Ginorsoldecex = s(10,s(10,100,8),10) (311) Ginorsoloctexidecex = s(10,ginorsoloctex,10) (312) Gargansoldecex = s(10,s(10,100,9),10) (313) Gargansolennexidecex = s(10,gargansolennex,10) (314) Googonsoldecex = s(10,s(10,100,10),10) (315) Googonsoldudecex = s(10,googonsoldecex,10) ... We have finished the list for three entry arrays but there is still a huge part of notation left, with an equally large number of googolisms. Stayed tuned for Part II, covering 4-entry arrays. Category:Blog posts